Apparatus for generating hollow electron beams



May 7, 1957 A. HARRIS APPARATUS FOR GENERATING HOLLOW ELECTRON BEAMS Filged Aug. 24, 1951 TYPICAL CURVES OF FREQUENCY OF OSCILLATION vs LARMOR FREQUENCY B=2co /1+ 7 6 5 4 3 2 O 2 mtz: 5256? Q -oan ARBITRARY UNITS INVENTOR. LAWRENCE A. HARRIS ATTO RN EYS APPARATUS FOR GENERATING HOLLOW ELECTRON BEAMS Lawrence A. Harris, Gainesville, Fla., assignor to Research Corporation, New York, N. Y., a corporation of New York Application August 24, 1951, Serial No. 243,424

3 Claims. (Cl. 313-84) This invention concerns the production and focusing of axially symmetric hollow electron beams and more specifically the production and maintenance of such beams without the necessity for a magnetic field along the entire axis of the beam.

Many microwave vacuum tubes make use of an electron beam. In the past it has been common practice to use a strong magnetic field along the axis of such a beam in order to convert any undesirable radial motion into angular motion and thus keep the beam well focused. Many analyses, being founded on the idea of using a solid beam, assumed infinitely intense magnetic fields and much power has been wasted in producing fields which approximate this assumption. The power requirements for producing such a magnetic field along the entire axis of the beam have been on important part of the total requirements for these tubes.

In many cases, however, there is no inherent necessity to use a solid beam. In certain applications, even without considering questions of economy, a hollow beam may be more desirable. The apparatus necessarily involved in producing a hollow beam consists of an electron gun which is capable of producing the electron beam required, and an evacuated drift tube in which the beam travels, this latter being simply a piece of hollow metal tubing. Existing systems also commonly use a solenoid somewhat longer than the tube itself in order to produce a uniform longitudinal magnetic field in the tube. Excluding factors which may be introduced by the electron gun itself, an electron moving in 'the drift tube part of such apparatus would be influenced by a variety of forces. The gun produces axial velocity which the electron will maintain. At the same time, the density of the beams which are involved here is such that the electrons tend to react against each other. The net effect is a strong tendency for the beam to expand unless restrained by some other force, this tendency being known as the space charge effect. If the beam does start to expand, however, the electrons must cross the longitudinal lines of flux produced by the axial solenoid and in so doing the expansion is converted into rotation. One further influence which may be applied to an electron in a hollow beam would be the force of an electric potential which could be applied by placing another conductor inside the outer drift tube but inside the hollow beam and then keeping the two drift tubes at different voltages. The potential gradient thus set up would tend to force any given electron toward the more positive electrode.

It is the object of this invention to provide a simpler and more eificient and economical method of producing and maintaining a hollow electron beam. More specifically it is the object of this invention to enable the maintenance and focusing of such a beam without the use of a magnetic field along the axis ofthe beam.

To achieve these objects this invention contemplates States. Patent T ing through which the beam passes,said opening beingtraversed by flux having radial components, and a co-' axial drift tube in registration with the beam on the two' the use of an electron gun, a casing around the gun in which a magnetic flux is created having an annular openelectrodes of which there is a potential difference. It will be noted that this apparatus requires the-use of a magnetic field in the beam forming region only, thus making a simpler apparatus and eliminating the need for the main coils and power supplies now used. A further advantage is the fact that mechanical alignment between the magnetic field and the drift tube is no longer a problem, and the tube may be relatively easily-connected to radio frequency apparatus.

In the drawings illustrating the invention, Fig. 1 shows a longitudinal cross section schematically representing one form of the invention; Fig. 2 is a plot of angular frequency vs. a quantity proportional to the axial flux; Fig; 3 shows another form of the invention in which a solenoid is added to counteract stray flux permeating into the, area-of an incompletely shielded cathode.

Fig. 1 schematically illustrates the above-mentioned parts as follows: An electron gun consisting of an annular cathode 10 and an annular anode 20 are contained in the metal case (e. g. soft iron) 12. A flux producing device 14 (in this example a cylindrical permanent magnet) sets up in the shield a fiux which passes radially across the gap in the shield 18 through which the beampossible of any fringing magnetic flux. The inner and.

outer drift tube electrodes are denoted 22 and 24 respec tively and are insulated from each other and from the case. The entire apparatus is, of course, evacuated inthe standard manner. Since the figure is intended to be merely diagrammatic all leads are omitted.

In broad terms, the apparatus functions as follows.. Electrons emitted by the cathode are accelerated by the anode and are formed by the configuration of the gun into a beam. In this case a hollow configuration such as that which may be produced by a Pierce type gun is preferred. The beam so produced is sutliciently dense so that the reaction of one electron against another (i. e. space charge effects) would by themselves result in the beam beginning to expand and diffuse were other forces not applied.

Traditionally, a magnetic field having strong axial components is used to change radial motion into angular motion and form, in most cases, a relatively solid beam. In the present invention, however, the entire beam crosses radial flux before entering an annular waveguide passage, and in so doing the entire beam acquires a rotational velocity component about its' axis which varies with radius, after which it enters the drift tubes upon which a potential difference exists (imposed, for example, by the battery 23) tending to force the electrons inward. Axial components of flux used in existing systems for focusing dense beams are unnecessary, focusing being instead accomplished by the carefully combined effect of radial flux in the beam focusing region and a potential, dif-. ference on the coaxial drift tubes which form the waveguide passage.

Neglecting interaction between electrons other than that tending to produce expansion, each electron in such a system is acted on by three forces; namely, the space charge eifect, the centrifugal force due to the rotation acquired from the magnetic field, and the force of the applied electric field. The first; two tend to force expansion whereas the latter counteracts this tendency. However, the gradients are not the same for the different l atented May 7, 1957 fdrcesapplied, and inorder' to produce stability and hence a focusing effect the density of the beam'must adjust itself in such a way that the gradient due to space charge effects just balances those from the other applied forces. The charge distribution which achieves this result is one in which the electrons are concentrated quite-heavily on the inside of the beam. While in some cases this may be a severe limitation, it may alsobe an advantage. For example, it would be very efficient in a coaxial type of traveling wave tube if the inner electrode rather than the outer one were corrugated to slow the wave.

The feasibility of the above methodof focusing-may be explained by the necessity for the beam to conserve energy. The beam does not have enough energy to expand, and it cannotcollapse because of therequirement for conservation of angular momentum. A mechanical analogy might be that of a ball-spinning-aroundthesides of a bowl in a gravitational field, for a similar balance of forces keeps the ball at some radius part way up the sides of the bowl. This description of the focusing effect neglects certain details such as possible ionization effects, interaction of electronsdue to their trajectories crossing radially, and the like, since these factors need not be of critical importance.

'I vo fundamental laws, conservation of energy and conservation of angular momentum, determine the be havior 'of'the electrons in the bea'inand thereforethe beam itself. If we assume a cylindrical-system of co ordinates wherein z is the position along the longitudinal axis, r is the radius, and 8 the angle involved, then The dot' not'ation indicates time derivatives, e'is the charge on the electron (-l'6 -l0-' coulomb); m is the electron mass (9.1 X 10 kg). 'cp is the electric potential of the point as measured from the cathode. All electrodes and potentials are independent of and 2, as is the magneticfield, for the analysis starts with the assumption of an axial magnetic field. The magnetic field due to the beam current is ignored and the electrons are assumed to have --started with-zero velocity (i. e. no velocity of emission) so that the velocity will dependon the anodes accelerating voltage V.

For analysis purposes the beamis assumed 'to consist o'fa series of cylindrical sh'ells withno radial crossing, each shell enclosing the sautecharge. Each electron is intact dependent on the course of every other electron; however, such a system wouldnot be subject to analysis. In order to havesuch a system it is necessary to approximate the true system by assuming a radius at which equilibrium is possible.

Making the above assumption'and using known mathematical procedures the following equation may be derived:

2 "3 5) (pf i V where e is a coefficient giving the magnitude and direc tion of the radial electric field, 'y is the average potential at r,,, r,, is the equilibrium radius at which thte electrons of a shell experience no radial force, V is the accelerating voltage,

and l "denotes the 'fiux (subscript c denotes cathode).

The equation for radialacceleration may then be found from the derivative of the above equation. Further 'calculation (including in approximating 2111-- To which equals R R a. es-

'4 results 'in the following equation'for angular frequency ofradial oscillation where a 5: i e/m ZOE-E a ,nnd K H o This equation is of considerable significance. In a stable beam 8 as defined above must be real. A plot t (as) e pa 2" 'Ta' o '2 l m Tr.) [Quichen 2)] where I is the beam current, p is the linear charge density of the beam, p 'and p, are the inner and outer electrode potentials, r and r are the inner and outer beam radii, and e is the permittivity of free space arXlO farads/meter). The same equations for charge density, magnetic field strength, and difference between electrode voltages may be obtained by balancing radial electric, centrifugal, and magnetic forces; however, the actual voltage of the inner electrode (go V), is, of necessity,

derived from the energy balance.

7 Typical design parameters derived from these calculations are as follows:

Aneirperimehtal-model showed maximum focusing at values'whieh were in close agreement with the above calculations o, being 1870 volts and go, 1175 volts.

The efiectiveness of these parameters is based on the assumption that the cathode region is completely shielded from stray flux, and that all the flux passes through the annular gap in the shield. While placing the air gap sufiiciently far forward of the anode should reduce fringing to negligible amounts, it may be useful under certain conditions to place a short solenoid over the entire gun structure to produce a field capable of compensating for and neutralizing any stray flux in the cathode region. Fig. 3 illustrates this procedure, the solenoid being designated 30. It will be noted'that the charge density of the beam varies as l/r,,*. This means that if the currently preferr'ed Pierce type gun is used, in which the cathode emits electrons in such a way as to produce a uniform beam, there is a shift of charge density toward the inside during the transient region. However, where the gun 'isshi'elded' the transition region (flux gap) is likely to be short, and this phenomenon should not materially influenee focusing.

Asheretofore-not'ed the foregoing analysis depends on certain assumptions, of which the only seriously questionabl'e one is the assumption of no radial crossing. This means that'the shells must have the same wavelength and phase and hence that 9 must be the same for all shells and independent of r or of R,,. If the density is non-uniform the frequency is not independent of r,,, and the assumption of no radial crossing is unjustified when oscillations take place. However, those conclusions are valid for equilibrium conditions, and have been verified by experiment.

Having thus described my invention, I claim:

1. Electron beam device comprising means for generating a hollow electron beam comprising an annular cathode, an accelerating anode having an annular aperture, a magnetic shield for said cathode and anode, an annular gap in said shield coaxial with the cathode and anode and aligned with the annular aperture in the anode to provide an exit aperture for the electron beam, means for generating magnetic flux across the annular gap in the shield to cause the electron beam traversing said gap to be subjected substantially exclusively to radial flux, cylindrical coaxial conductive elements aligned with the aixs of cathode, anode and flux gap and forming an annular passage for the emitted beam, and means for maintaining a potential diiference between said coaxial elements.

2. Electron beam device comprising means for generating a hollow electron beam comprising coaxial magnetic structure having an annular gap at one end, an electron-emitting annular cathode within the magnetic structure and shielded thereby, an anode disposed within the magnetic structure intermediate the cathode and the annular gap in the shield, means for generating magnetic flux across the annular gap in the shield to cause the electron beam traversing said gap to be subjected substantially exclusively to radial flux uniformly distributed about the beam axis, thereby to impart to the electron substantially uniform tangential velocity about said beam axis, cylindrical coaxial conductive elements out- Wardly of the shield and axially disposed relative to the annular gap to define an annular wave guide passage for the electron beam emitted from the gap, and means for maintaining a potential ditlerence between said 00- axial elements to generate uniform inwardly-directed electrostatic forces on said electron beam along its axis.

3. Electron beam device comprising means for generating a hollow electron beam comprising coaxial magnetic structure containing electron emitting and accelerating means, said magnetic structure comprising a cylindrical shield, a central, axially directed member, an annular gap between the cylindrical shield and the central axially directed member at one end, the other end of the structure being closed to form a flux path between shield and central member, and means for generating magnetic flux across said annular gap, the electron emitting and accelerating means comprising a cathode and anode encircling the central axially directed member for directing an annular electron beam through the annular gap to cause the beam to be subjected substantially exclusively to radial magnetic fiux relative to the beam axis, cylindrical coaxial conductive elements aligned with the axis of cathode, anode and flux gap and forming an annular passage for the emitted beam, and means for maintaining a potential difierence between said coaxial elements.

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